V.

System of The Copernican Syftem easily accounts for all the Celestial Phenomena, Ticho Brahe and tho' Obfervation and Argument are equally favourable to it, yet TichoBrabe an eminent Philofopher of that Age refufed his affent to the Evidence of thefe Difcoveries, whether deluded by an ill-formed Experiment, (b) or carried away by the Vanity of making a new Syftem, he composed one which steers a middle Course between thofe of Ptolomy and Copernicus ; he fuppofed the Earth to be at rest and the other Planets which moye round the Sun, to revolve with him round the Earth, in the Space of 24 Hours; thus retaining the most exceptionable Part of Ptolomy's Syftem, viz. the inconceivable Rapidity with which the primum Mobile is fuppofed to revolve, from whence we may learn into what dangerous Errors the mifapplication of Genius may lead us.

The Difco

Tho' Tycho erred in the Manner he made the Celestial Bodies move, veries relayet he contributed very much to the Progrefs of the Discoveries relative to Syftem of the Syftem of the World, by the Accuracy and long Series of his Obfervathe World, tions. He determined the Pofition of a vaft Number of Stars to a Degree of improved exactnefs unknown before; he difcovered the Refraction of the Atmosphere, by Tycho. by which the Celestial Phenomena are so much influenced; he was the first who proved from the Parallax of the Comets, that they afcend above the Moon; he was the first who obferved what is called the Moon's variation; and in fine, it is from his Obfervations on the Motions of the Planets, that Kepler who refided with him, near Prague, during the laft Years of his Life, deduced his admirable Theory of the Motions of the Heavenly Bodies.

be difcover

VI.

How much Copernicus undoubtedly rendered important Services to Human Reafon remained to by re-establishing the true Syftem of the World: It was already a great ed after Co-point gained that Human Vanity condefcended to place the Earth in the Numpernicus. ber of the fimple Planets; but much still remained to be discovered: neither the Forms of the Planetary Orbits, nor the Laws by which their Motions. are regulated, were known; for thefe important Difcoveries we are indebted to Kepler.

(b) It was objected to Copernicus, that the Motion of the Earth would produce Effects which did not take Place; that, for Example, if the Earth moved, a Stone dropp'd from the Top of a Tower, ought not to fall at the Foot of it, because the Earth moved during the Time of the Stone's defcent, that notwithstanding it falls at the Foot of the Tower. COPERNICUS replied, that the Situation of the Earth with refpect to Bodies that fall on its Surface was the. fame as that of a Ship in Motion, with respect to Bodies that are made to fall in it; he afferted, that a Stone let fall from the Top of the Maft of a Veffel in Motion, would fall at the Foot of it. This Experiment which is now inconteftible was then ill-made, and was the Canis. or the Pretext which made Ticho refuse his afsent to the Discoveries of Copernicus.

Discoveries

This eminent Philofopher found out, that the Notion which generally prevailed before his time, that the Planets revolved in circular Orbits, was er- of Kepler roneous; and he discovered, by the means of Ticho's Obfervations, that the el pticity the Planets move in Ellipfes, the Sun refiding in one of the Foci : and that of the orbits. the properthey move over the different Parts of their Orbit, with different Velocities, fo tionality of that the Area defcribed by a Planet, that is, the Space included between the the areas and straight lines drawn from the Sun to any two Places of the Planet, is always the times. proportional to the time which the Planet employs to pafs from one to the other.

Relation

Some years afterwards, comparing the Times of the Revolutions of the different Planets about the Sun, with their different Distances from him, he which fubfound that the Planets which are placed the fartheft from the Sun to move fifts between floweft, and examining whether this Proportion was that of their Distances, the periodic he discovered after many Trials, in the Year 1618, that the Times of the diftantheir Revolutions were as the Square Roots of the Cubes of their mean ces. Distances from the Sun.

VII.

Kepler not only discovered these two Laws, which retain his Name, and which regulate the Motions of all the Planets, and the Curve they defcribe, but had also fome Notion of the Force which makes them describe this Curve; in the Preface to his Commentaries on the Planet Mars, we discover the first Hints of the attractive Power; he even goes fo far as to fay, that the Flux and Reflux of the Sea, arifes from the gravity of the Waters towards the Moon: but he did not deduce from this Principle what might be expected from his Genius and indefatigable Industry. For in his Epitome of Astronomy(c) he proposes a phyfical Account of the planetary Motions from quite different Principles; and in this fame Book of the Planet Mars, he supposes in the Planets a friendly and a hoftile Hemisphere, that the Sun attracts the one and repels the other, the friendly Hemisphere being turned to the Sun in the Planets descent to its Perhihelium, and the Hoftile in its Recefs.

VIII..

The Attraction of the Celestial Bodies was fuggested much more clearly by M. Hook, in his Treatife on the Motion of the Earth, printed in the Year 1674, twelve Years before the Principia appeared. These are bis Words, Page 27, "I fhall explain hereafter a Syftem of the World, different in ma"ny Particulars from any yet known, anfwering in all Things to the com"mon Rules of Mechanical Motions. This depends on the three following "Suppofitions."

(c) See Gregory, Book 1, Page 69.

Singular at That all celeftial Bodies, whatever, have an Attraction, or gravitating: necdote con- Power towards their own Centers, whereby they attract, not only their traction. "own Parts and keep them from flying from them, as we may obferve the

cerning at

Strange no

66

Earth to do, but that they do alfo attract all the other celestial Bodies that are within the Sphere of their Activity; and confequently not only the "Sun and the Moon have an Influence upon the Body and Motion of the "Earth, and the Earth on the Sun and Moon, but alfo, that Mercury, Venus, Mars, Jupiter aud Saturn, by their attractive Powers, have a confi"derable Influence upon the Motion of the Earth, as in the fame Manner"the correfponding attractive Power of the Earth hath a confiderable influ 66 ence upon the Motion of the Planets."

"2d That all Bodies whatever that are put into a direct and fimple Motion, "will fo continue to move forward in a ftreight Line, till they are by fome "other effectual Power deflected and turned into a Motion, defcribing a Cir"cle, an Ellipfe, or fome other more compounded Curve Line."

66

3d That thefe attractive Powers are fo much the more powerful in ope"rating, by how much the nearer the Body wrought upon is to their own. "Center."

"These feveral Degrees I have not yet experimentally verified, but it is. "a Notion which if fully profecuted as it ought to be, will mightily affift the "Aftronomer to reduce all the celeftial Motions to a certain Rule, which I

doubt will never be done true without it. He that understands the Na-"ture of the circular Pendulum and circular Motion, will eafily understand: "the whole Ground of this Principle, and know where to find Directions "in Nature for the true ftating thereof. This I only hint at present to fuch as have a Capacity and Opportunity of profecuting this Enquiry, &c."

IX.

We are not to imagine, that this Hint thrown out cafually by Hook, detracts from the Glory of Newton, who even took Care to make Mention of it in his Book de Syftemate mundi (d). the Example of Hook and Kepler makes us perceive the wide Difference between having a Notion of the Truth, and being able to eftablish it by irrefragable Demonstration; it alfo fhews us how little the greatest Sagacity can penetrate into the Laws and Conftitution of Nature, without the Aid and Direction of Geometry..

X.

Kepler, who made fuch important Discoveries, whilft he followed this untions of Keperring Guide, affords us a convincing Proof of the Errors into which the brighteft Genius may be feduced, by indulging the pleasing Vanity of inventing Systems; who could believe, for Inftance, that fuch a Man could

ler.

page. 3 Edition of 1731.

adopt the wild Fancies and whimfical Reveries of the Pythagoreans, concerning Numbers: yet he thought that the Number and Interval of the primary Planets bore fome Relation to the five regular Solids of Elementary Geometry (e), imagining that a Cube infcribed in the Sphere of Saturn would touch the Orb of Jupiter with its fix Planes, and that the other four regular Solids, in like Manner, fitted the Intervals that are betwixt the Spheres of the other Planets: afterwards on difcovering that this Hypothefis did not fquare with the Distances of the Planets, he fancied that the celeftial Motions are performed in Proportions correfponding with thofe, according to which a Cord is divided in order to produce the Tones which compofe the Octave in Mufic (f);

Kepler having fent to Ticho a Copy of the Work, in which he attempted to establish thofe Reveries. Ticho recommended to him, in his An- Wife coun fwer(g), to relinquish all Speculations deduced from firft Principles, all rea- fel of Ticho foning a Priori, and rather study to establish his Researches on the fure and to Kepler.

firm Ground of Observation.

notion of

Hughens.

The great Hugbens himself (h) believed that the fourth Satellite of Saturn, Whimfical which retains his Name, making up with our Moon and the four Satellites of Jupiter fix fecundary Planets, the Number of the Planets was complete, and it was labour loft to attempt to difcover any more, because the principle Planets are alfo fix in Number, and the Number Six is a perfect Number, as being equal to the Sum of its aliquot Parts, 1, 2 and 3.

XL.

It was by never deviating from the moft profound Geometry, that Newton difcovered the Proportion in which Gravity acts, and that in his Hands the Principle of which Kepler and Hook had only fome faint Notion, became the Source of the most admirable and unhoped for Discoveries.

Advantages

over Kepler

One of the Causes which prevented Kepler from applying the Principles of Newton of Attraction to explain the Phænomena of Nature with Succefs, was his in his time, Ignorance of the true Laws of Motion. Newton had the Advantage over the theory of Kepler of profiting of the Laws of Motion, eftablished by Hughens, which motion was he has carried to fo great a Height in his Mathematical Principles of Natu- derftood. ral Philofophy.

XII.

better un

the principia

The Mathematical Principles of Natural Philofophy confift of three Analyfis of Books, befides the Definitions, the Laws of Motion and their Corollaries; the firft Book is compofed of fourteen Sections, the fecond contains nine,

(e) Mysterium Cofmographicum.

(f) Mysterium Cofmographicum.

(g) Uti fufpenfis fpeculationibus a priori defcendentibus animum potius ad obfervationes quas fimul offerebat confiderandas adjicerem (it is Kepler who fpeaks) note in fecundam.. editionem myfterii cosmographici

and the third, the Application of the two first to the Explication of the Phoenomena of the Syftem of the World.

XIII.

The Principia commence with eight Definitions; Newton fhews in the Definitions. two first how the Quantity of Matter and the Quantity of Motion fhould be measured; he defines in the third, the Vis intertia, or refifting Force, which all Matter is endued with; he explains in the fourth what is to be understood by active Force; he defines in the fifth the centripetal Force, and lays down in the fixth, feventh and eighth the Manner of measuring its abfolute Quantity, its motrix Quantity, and its accelarative Quantity; afterwards he establishes the three following Laws of Motion.

XIV.

Laws of mo 1ft. That a Body always perfeveres of itself, in its State of Reft, or of uniform Motion in a straight Line.

Lion.

First book,

the ift fecti

2d. That the change of Motion, is proportional to the Force impreffed, and is produced in the ftraight Line in which that Force acts.

3d. That Action and Reaction are always equal with oppofite Direations.

XV.

Newton having explained thofe Laws, and deduced from them feveral on contains Corollaries, commences his firft Book with eleven Lemmas, which comthe princi pofe the first Section, he unfolds in those eleven Lemmas his Method of ples of infiPrime and ultimate Ratios; this Method is the Foundation of infiniteffimal geometry Geometry, and by its Affiftance, this Geometry is rendered as certain as that of the Ancients.

niteffimal

the other 13

The thirteen other Sections of the first Book of the Principia, are employgeneral pro-ed in demonftrating general Propofitions on the Motion of Bodies, Abitracpofitions on the motion ting from the Species of these Bodies and of the Medium in which they

of bodies. move.

It is in this firft Book that Newton unfolds all his Theory of the gravitation of the celeftial Bodies, but does not confine himself to examine the Questions relative to it; he has rendered his Solutions general, and has given a great Number of Applications of thofe Solutions.

XVI.

Second book In the fecond Book, Newton treats of the Motion of Bodies in refifting it treats of the motionof Mediums. bodies in re- This fecond Book which contains a very profound Theory of Fluids, and fifting me- of the Motion of Bodies which are immerfed in them, feems to have been intended to destined to over throw the System of Vortices, though it is only in the Scholioverthrow um of the last Propofition,that Newton openly attacks Defcartes, and proves of Defcartes that the celestial Motions are not produced by Vortices.

diums.

the vortices